2. Object-Space Visibility Culling Anthony Steed University College London Based upon material presented by Claudio T. Silva at Eurographics 1999 Slides, and material for slides, have been provided by Satyan Coorg (MIT/IBM), Sigal Dahan and Dudu Sayag (Tel-Aviv)

3. Approximate Visibility Determination Develop algorithms that are output sensitive, that is, complexity depends on the number of visible polygons, not the total number of polygons. Drop the exact visibility requirement, and instead attempt to develop algorithms that estimate the triangles which have visible fragments In this talk, we will speak about algorithms that overestimate the visible fragments, the so called conservative visibility algorithms

4. Talk Summary Cells and portals –Teller and Sequin, Siggraph 91 –Luebke and Georges, I3D 95 Visibility culling with large occluders –Coorg and Teller, SoCG 96 and I3D 97 –Hudson et al, SoCG 97

5. Talk Summary Cells and portals –Teller and Sequin, Siggraph 91 –Luebke and Georges, I3D 95 Visibility culling with large occluders –Coorg and Teller, SoCG 96 and I3D 97 –Hudson et al, SoCG 97

6. The Cells-and-Portals Approach (1) Decompose space into convex cells (2) For each cell, identify its boundary edges into two sets: opaque or portal (3) Precompute visibility among cells (4) During viewing (eg, walkthrough phase), use the precomputed potentially visible polygon set (PVS) of each cell to speed-up rendering

7. Space Subdivision Input Scene: Convex subdivision: Generated by computing a k-d tree of the input faces

8. Determining Adjacent Information

9. Computing the PVS of a cell SL  0,  L  L SR  0,  R  R Linear programming problem: Find_Visible_Cells(cell C, portal sequence P, visible cell set V) V=V  C for each neighbor N of C for each portal p connecting C and N orient p from C to N P’ = P concatenate p if Stabbing_Line(P’) exists then Find_Visible_Cells (N, P’, V)

10. Eye-to-Cell Visibility The eye-to-cell visibility of any observer is a subset of the cell-to-cell visibility for the cell containing the observer

11. Eye-to-Cell Visibility A cell is visible if –cell is in VV –all cells along stab tree are in VV –all portals along stab tree are in VV –sightline within VV exists through portals

12. Results

16. Talk Summary Cells and portals –Teller and Sequin, Siggraph 91 –Luebke and Georges, I3D 95 Visibility culling with large occluders –Coorg and Teller, SoCG 96 and I3D 97 –Hudson et al, SoCG 97

17. Luebke and Georges, I3D 95 Instead of pre-processing all the PVS calculation, it is possible to use image-space portals to make the computation easier Can be used in a dynamic setting

18. Luebke and Georges, I3D 95

20. Talk Summary Cells and portals –Teller and Sequin, Siggraph 91 –Luebke and Georges, I3D 95 Visibility culling with large occluders –Coorg and Teller, SoCG 96 and I3D 97 –Hudson et al, SoCG 97

21. When does A occludes B ?

22. A B Convex Occluers A B A occludes B B is not occluded C A B

23. Important Events e A v B e A v B

24. Naïve Algorithm For all combinations of edges and vertices find the corresponding plane –  (n 2 ) planes Partition space by these planes –  (n 6 ) cells

25. Relevant Planes Only a small selection of planes are actually relevant For complete objects - consider the silhouettes v e Plane ve separates A and B A B All silhouette edges produce supporting planes

26. For Individual Polygons Track Visibility Changes –Track all planes defined by E and vertices in edge from B that intersect E

27. For Individual Polygons Non-edge cases Track planes –V7,V3,V5 –V7, V5, V6 –V7, V6, V3 Overall this is  (n+m) for an object pair

28. For N Objects Reduce complexity from  (n 2 ) by using an octree structure

29. Hierarchical Tests

32. Optimising the Octree Traverse Not feasible to compute visibility relationship for whole octree each time viewpoint moves Re-use the idea of tracking the separating planes –Do this for each octree cell on boundary –Note that a cell visibility can only become visible if its parent is partially visible

33. Dynamic Plane Maintenance First approach –find a sub-set of close planes and test only those if viewpoint does not move more than r

34. Dynamic Plane Maintenance Second approach –keep the planes themselves in an octree –in each octree cell keep a list of intersecting planes –a cell-cell traversal through the octree goes via the LCA, adding and deleting planes no possibility of repeating an add or delete, so this is strictly better than naïve recomputation with worst case being situations where LCA is root

35. Coorg and Teller, I3D 97 Ignored A B T Added the capability to join the effect of connected occluders, that is, a form of occluder fusion

36. Occluder Fusion

37. Fast Tangent Plane Computation

39. Because this computation is fast, it is no longer necessary to keep fine-grain visibility events

40. Use Temporal Coherence to Cache Relevant Events

41. Choosing Occluders Pick large occluders close to the viewpoint –Good for application to octree scene structure Pick smaller occluder that are close to objects (detail occluders) –I.E. they occlude an object most of the time –Applied only to a specified object, not to the general scene octree

42. Detail Occluders

43. Metric for Comparing Occluder Quality Occluder quality: (-A (N * V)) / ||D|| 2 A : the occluder’s area N : normal V : viewing direction D : the distance between the viewpoint and the occluder center Large polygon have large area-angle.

44. Results

45. The percentage of polygons draw The culling and drawing times (in milliseconds)

46. Talk Summary Cells and portals –Teller and Sequin, Siggraph 91 –Luebke and Georges, I3D 95 Visibility culling with large occluders –Coorg and Teller, SoCG 96 and I3D 97 –Hudson et al, SoCG 97

47. Hudson et al, SoCG 97 C B A Viewpoint Occluder

48. Occluder Storage Partition model into cells and store good occluders in the cells Identify likely occluders for a cell –they subtend a large solid-angle (similar to Coorg and Teller) Test likely occluders –use a sample of viewpoints and compute actual shadow volumes resulting

49. Occluder Usage At run-time –form shadow volumes from likely occluders –do view-volume cull and shadow-volume occlusion test in one pass across the spatial sub- division of the scene –each cell of the sub-division is tested for inclusion in view-volume and non-inclusion in each shadow volume

50. Occluder Test Overlap test (cell to shadow volume) is performed in 2D –If the subdivision uses bounding boxes, then a very efficient overlap test is presented

51. Conclusions Cells and portals –Gives excellent results IF you can find the cells and portals –Good for interior scenes –Identifying cells and portals is often done by hand General polygons models “leak”

52. Conclusions Visibility culling with large occluders –Very good for outdoor (city) scenes where occluders are large and depth complexity can be very high –Not good for indoor scenes in general since there are many small occluders that would need to be fused